Existence of optimal controls for control systems governed by nonlinear partial differential equations
Existence of optimal nonanticipating controls in piecewise deterministic control problems
Optimal nonanticipating controls are shown to exist in nonautonomous piecewise deterministic control problems with hard terminal restrictions. The assumptions needed are completely analogous to those needed to obtain optimal controls in deterministic control problems. The proof is based on well-known results on existence of deterministic optimal controls.
Existence of optimal solutions in general discrete systems
Existence of pole-zero structures in a rational matrix equation arising in a decentralized stabilization of expanding systems
A necessary and sufficient condition for the existence of pole and zero structures in a proper rational matrix equation is developed. This condition provides a new interpretation of sufficient conditions which ensure decentralized stabilizability of an expanded system. A numerical example illustrate the theoretical results.
Existence of solution to transpiration control problem.
Existence of solutions and approximate controllability of impulsive fractional stochastic differential systems with infinite delay and Poisson jumps
The paper is motivated by the study of interesting models from economics and the natural sciences where the underlying randomness contains jumps. Stochastic differential equations with Poisson jumps have become very popular in modeling the phenomena arising in the field of financial mathematics, where the jump processes are widely used to describe the asset and commodity price dynamics. This paper addresses the issue of approximate controllability of impulsive fractional stochastic differential...
Existence of solutions and controllability of nonlinear integro-differential systems in Banach spaces.
Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory
In this paper, we study ϕ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multi-valued right-hand side. The nonlinearity satisfies either a Nagumo-type growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively. Two applications to a problem from control theory are...
Existence theorem for nonconvex stochastic inclusions.
Existence theorems for some optimal control problems
Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays.
Existenzsätze in der Theorie der Matrizen und lineare Kontrolltheorie.
Explicit conditions for ripple-free dead-beat control
Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model
We analyze the optimal sales process of a stochastic advertising and pricing model with constant demand elasticities. We derive explicit formulae of the densities of the (optimal) sales times and (optimal) prices when a fixed finite number of units of a product are to be sold during a finite sales period or an infinite one. Furthermore, for any time t the exact distribution of the inventory, i.e. the number of unsold items, at t is determined and will be expressed in terms of elementary functions....
Explicit solutions of regular linear discrete-time descriptor systems with constant coefficients.
Exponential admissibility and dynamic output feedback control of switched singular systems with interval time-varying delay.
Exponential convergence for a convexifying equation
We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573–1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.
Exponential convergence for a convexifying equation
We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573–1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.
Exponential convergence for a convexifying equation
We consider an evolution equation similar to that introduced by Vese in [Comm. Partial Diff. Eq. 24 (1999) 1573–1591] and whose solution converges in large time to the convex envelope of the initial datum. We give a stochastic control representation for the solution from which we deduce, under quite general assumptions that the convergence in the Lipschitz norm is in fact exponential in time.
Exponential filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays
This paper is concerned with the exponential filter design problem for stochastic Markovian jump systems with time-varying delays, where the time-varying delays include not only discrete delays but also distributed delays. First of all, by choosing a modified Lyapunov-Krasovskii functional and employing the property of conditional mathematical expectation, a novel delay-dependent approach is developed to deal with the mean-square exponential stability problem and control problem. Then, a mean-square...